Making a six-part mould- Cutting by planes
The question is simple but the answer is a bit complex.

How does boolean modifier work

The boolean modifier can do 3 boolean operations between 2 solid objects.
They are simple and fully described here.
The point I want to focus to is that they both need to be solid. They cannot be a cube and a plane, because the operations (union, difference and intersection) operate on volumes, not on faces/edges/vertices.

In my example the situation is simple, because I'm going to use only one plane. To do it in your case you will need to repeat this instructions recursively for every cut.

Extruding planes to give them a volume and using the Boolean modifier

This image shows a cube and a plane.


I want to use the plane as a "blade" to cut the cube in two parts.
So I select the plane and go to edit-mode:


I extrude it to have a volume that completely covers one of the two parts of the cube:


I go back to object-mode, hide (presing H) the extruded plane, I select the cube and add a boolean modifier to it.
In the modifier settings i choose the extruded plane as the "Object" I want to use to do the boolean.

As "Operation" I can choose "Difference" to obtain one of the two parts:


...or the "Intersection" to obtain the other part:


To have them both I need to duplicate the cube and apply the "Difference" boolean modifier to the first and the "Intersection" to the other.

You'll need to do this steps with the first part to divide the first object in two, and then to repeat them recursively on the pieces you obtained to divide them again, until you have all the pieces.

I know it's a struggle, but I don't know other ways to do this.